WPI Worcester Polytechnic Institute

Computer Science Department
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CS4341 Introduction to Artificial Intelligence 
Project 2 - C 2002
Solutions to Part I

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Part I

Forward Chaining

RULE PREMISES                   TREE
---------------------------------------------------------------
R1 

Asset ?x low			Asset (?x) bob low
Salary ?x low				|
				salary (?x) bob low
				Succeeds
				WM <--WM U {credit bob bad}
---------------------------------------------------------------
R2

Asset ?x low			asset (?x)bob low
Salary ?x high				|
				salary (?x)bob high
				Fails against WM
---------------------------------------------------------------
R3

Asset ?x high			asset (?x)sue high
				Succeeds
				WM <--WM U {credit sue good}

---------------------------------------------------------------
R4
                                               
                                                /  \
                                               /    \
                                              /      \
Asset ?x ?y		asset (?x)bob (?y)low		asset (?x)sue (?y)high
				|				|
			married (?x)bob (?z)mary	married (?x)sue (?z)bill
			succeeds			succeeds
			WM <--WM U {asset mary low}	WM U{asset bill high}

Working memory now is:

salary bob low
asset bob low
married bob mary
parent bob bill
asset sue high
married sue bill
credit bob bad
credit sue good
asset mary low
asset bill high

Second pass
---------------------------------------------------------------
R1
                                                /  \
                                               /    \
                                              /      \
Asset ?x low		asset (?x)bob low		asset (?x)mary low
				|				|
			salary (?x)bob low		salary (?x)mary low
		(credit bob bad already in WM)		 Fails against WM
---------------------------------------------------------------
R2

                                                /  \
                                               /    \
                                              /      \
Asset ?x low		asset (?x)bob low		asset (?x)mary low
Salary ?x high			|				|
			salary (?x)bob high		salary (?x)mary high
			Fails against WM (again)	fails against WM
---------------------------------------------------------------
R3
                                                /  \
                                               /    \
                                              /      \
Asset ?x ?y		asset (?x)sue high 		asset (?x)bill high
			Success				Success
		(credit sue good already in WM)		WM <--WM U {credit bill good}
---------------------------------------------------------------
R4
                  /       |                 |            \
                 /        |                 |             \
                /         |                 |              \
asset bob low     asset sue high     asset mary low     asset bill high
        |                 |                 |               |
married bob mary  married sue bill   married mary ?z    married bill ?z

succeeds          succeeds succeeds  fails againt WM    fails against WM 
{asset mary low   {asset bill high   
already in WM}     already in WM}   


Working memory now is:

salary bob low
asset bob low
married bob mary
parent bob bill
asset sue high
married sue bill
credit bob bad
credit sue good
asset mary low
asset bill high
credit bill good


Third Pass
No changes

Final working memory is:

salary bob low
asset bob low
married bob mary
parent bob bill
asset sue high
married sue bill
credit bob bad
credit sue good
asset mary low
asset bill high
credit bill good


Backward Chaining

G1:					credit bob good
				/				\	
---------------------------------------------------------------------------
R2
Asset ? low		asset (?x)bob low			|				
			(succeeds) 				|
salary ?x low		salary (?x)bob low			|
			Fails against WM and rules		|
								|
---------------------------------------------------------------------------
R3								|
Asset ?x high						asset (?x)bob high
								|
----------------------------------------------------------------------------
R4							asset (?x)sue (?y)high
								|
							married (?x)sue (?z)bob
							Fails against WM and rules
						
								

G2:				credit mary bad
					|
---------------------------------------------------------------------------
R1					|
Asset ?x low			asset (?x)mary low		
Salary ?x low				|		
					|
--------------------------------------------------------------------------
R4					|
Asset ?x ?y			asset (?x)bob (?y)low
Married ?x ?z(mary)		married (?x)bob (?z)mary
Success				WM <--WM U {asset mary low}
					|
--------------------------------------------------------------------------				
(go back to continue with R1)
R1					|
				salary (?x)mary low
				Failes agains WM and Rules
--------------------------------------------------------------------------